Generalizing Subspace Codes to Flag Codes Using Group Actions

Dirk Liebhold; Gabriele Nebe; María Ángeles Vázquez-Castro

doi:10.1007/978-3-319-70293-3_4

Generalizing Subspace Codes to Flag Codes Using Group Actions

Dirk Liebhold, Gabriele Nebe, María Ángeles Vázquez-Castro

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© 2018, Springer International Publishing AG. In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.

Idioma original	Anglès
Títol de la publicació	Signals and Communication Technology
Pàgines	67-89
Nombre de pàgines	22
ISBN (electrònic)	1860-4870
DOIs	https://doi.org/10.1007/978-3-319-70293-3_4
Estat de la publicació	Publicada - 1 de gen. 2018

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10.1007/978-3-319-70293-3_4

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AB - © 2018, Springer International Publishing AG. In this chapter, we first discuss structural properties of subspace codes by applying group actions. We will see that the projective space, the Grassmannian and the Schubert cells can be realized by looking at the orbits of certain linear groups on matrices. The approach naturally leads to a generalization, where we replace subspace codes with flag codes. We describe and analyze a channel model for these new codes that is similar to the operator channel introduced by Koetter and Kschischang, give examples of flag codes and discuss how to compute sphere packing and sphere covering bounds for flag codes.

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Generalizing Subspace Codes to Flag Codes Using Group Actions

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